Complexity

While chaos is the study of how simple systems can generate complicated behavior, complexity is the study of how complicated systems can generate simple behavior.Complex systems are spatially and/or temporally extended nonlinear systems characterized by emergent collective properties.

Cellular Automata

(John von Neumann, S. Ulam, and S. Wolfram)

What they are

Game of Life

NxNxN...xN matrix of cell values (that can be real or imaginary values) that change over time according to 1) the status of 'neighbors' (or 'connected' cells, or some external condition) and 2) some rule, which can be global (as here) or local. This 'system' 'evolves' over time.

Rules

NNeighbors>3 ->0 (overcrowding)

NN<2 -> 0 ("loneliness")

NN=2 retain current state

NN=3->1 (staying alive or birth)

These system have "attractors"

static states - "fixed point"

periodic states - "limit cycles"

nonperiodic states ("chaotic" or "strange attractor")

There are variations in rules, kinds of entities, ...Vivarium and LifeLab are examples (free or shareware).